Leave the potatoes whole, if small, or cut in half if large. Place in a large saucepan with salted water to cover by several inches. Bring to a simmer, cover partially and adjust heat to maintain a gentle simmer. Cook until a knife slips in easily, about 30 minutes. Drain, then return the potatoes to the warm pot. Return the pot to the heat and shake until any moisture evaporates.

While the potatoes cook, melt the butter in a small saucepan over moderate heat. Add the green garlic and sauté until softened, 3 to 5 minutes. If desired, add milk and cream. Put the boiled potatoes through a food mill or ricer. Add the hot milk mixture and stir vigorously with a wooden spoon until smooth. Taste and adjust seasoning